This research focuses on the modeling and simulation of combustion dynamics in lean-premixed gas-turbines engines. The primary objectives are: (1) to establish an efficient and accurate numerical framework for the treatment of unsteady flame dynamics; and (2) to investigate the parameters and mechanisms responsible for driving flow oscillations in a lean-premixed gas-turbine combustor.; The energy transfer mechanisms among mean flow motions, periodic motions and background turbulent motions in turbulent reacting flow are first explored using a triple decomposition technique. Then a comprehensive numerical study of the combustion dynamics in a lean-premixed swirl-stabilized combustor is performed. The analysis treats the conservation equations in three dimensions and takes into account finite-rate chemical reactions and variable thermophysical properties. Turbulence closure is achieved using a large-eddy-simulation (LES) technique. The compressible-flow version of the Smagorinsky model is employed to describe subgrid-scale turbulent motions and their effect on large-scale structures. A level-set flamelet library approach is used to simulate premixed turbulent combustion. In this approach, the mean flame location is modeled using a level-set G-equation, where G is defined as a distance function. Thermophysical properties are obtained using a presumed probability density function (PDF) along with a laminar flamelet library. The governing equations and the associated boundary conditions are solved by means of a four-step Runge-Kutta scheme along with the implementation of the message passing interface (MPI) parallel computing architecture. The analysis allows for a detailed investigation into the interaction between turbulent flow motions and oscillatory combustion of a swirl-stabilized injector. Results show good agreement with an analytical solution and experimental data in terms of acoustic properties and flame evolution. A study of flame bifurcation from a stable state to an unstable state indicates that the inlet flow temperature and equivalence ratio are the two most important variables determining the stability characteristics of the combustor. Under unstable operating conditions, several physical processes responsible for driving combustion instabilities in the chamber have been identified and quantified. These processes include vortex shedding and acoustic interaction, coupling between the flame evolution and local flow oscillations, vortex and flame interaction and coupling between heat release and acoustic motions. The effects of inlet swirl number on the flow development and flame dynamics in the chamber are also carefully studied. In the last part of this thesis, an analytical model is developed using triple decomposition techniques to model the combustion response of turbulent premixed flames to acoustic oscillations.
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